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New analytical solutions to a medium with completing weakly nonlocal nonlinearity and parabolic law nonlinearity by modified first integral method
In this article, we investigated certain medium with completing weakly nonlocal nonlinearity and parabolic law nonlinearity, which has recently...
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Perturbation of Systems with a First Integral: Motion on the Reeb Graph
We consider the long-time behavior of systems close to a system with a smooth first integral. Under certain assumptions, the limiting behavior, to...
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The exact solutions of conformable time-fractional modified nonlinear Schrödinger equation by first integral method and functional variable method
Using the first integral method (FIM) and the functional variable method (FVM), firstly we find the analytical solutions of conformable...
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Exact Solution to the Contact Problem in a Quarter-Plane of a Multilayer Medium by the Universal Simulation Method
AbstractIn this paper, for the first time, an exact solution to the contact problem posed on the surface of a multilayer medium in a quarter-plane is...
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Exact Solution of the Wiener–Hopf Equation on the Segment for Contact Problems of the Theory of Cracks in a Layered Medium
AbstractThis paper presents an approach that allows us for the first time to construct an exact solution of the Wiener–Hopf integral equations on a...
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Exact Methods of Solution: A Brief Survey
The preceding chapter contains a presentation of several equations, differential and integral ones, describing multiple scatterings of photons. In...
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The d’Alembert solution in hyperboloidal foliations
We explicitly construct the analogue of the d’Alembert solution to the 1+1 wave equation in an hyperboloidal setting. This hyperboloidal d’Alembert...
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Einstein–Maxwell equations: Solution-generating methods as “coordinate” transformations in the solution spaces
AbstractThe solution-generating methods discovered for integrable reductions of the Einstein and Einstein–Maxwell field equations...
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On the integral solution of hyperbolic Kepler’s equation
In a recent paper of Philcox, Goodman and Slepian, the solution of the elliptic Kepler’s equation is given as a quotient of two contour integrals...
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Solution of the Diffusion Equation in Free Space
In this chapter, we focus on solving the diffusion equation under no spatial constraints, that is, in free space, to find a unique solution that will...
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Carrollian structure of the null boundary solution space
We study pure D dimensional Einstein gravity in spacetimes with a generic null boundary. We focus on the symplectic form of the solution phase space...
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A constructive solution to the cosmological bootstrap
In this paper we revisit a generalised crossing equation that follows from harmonic analysis on the conformal group, and is of particular interest...
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Numerical solution, conservation laws, and analytical solution for the 2D time-fractional chiral nonlinear Schrödinger equation in physical media
The (2+1)-dimensional time-fractional chiral non-linear Schrödinger equation in physical media is considered in this paper. At the outset, the Lie...
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Hydrogen Atom Second Solution: Physical and Chemical Interpretations
We mainly study the ground state of the hydrogen atom in terms of the second kind of Legendre functions. We use a special self-adjoint transformation...
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Approximation of a Solution to the Stationary Navier–Stokes Equations in a Curved Thin Domain by a Solution to Thin-Film Limit Equations
We consider the stationary Navier–Stokes equations in a three-dimensional curved thin domain around a given closed surface under the slip boundary...
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A Kinematic Interpretation of Rigid Body Motion in a New Solution of Grioli Equations
AbstractA new solution is obtained for the problem concerning the motion of a rigid body having a fixed point, affected by potential and gyroscopic...
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On the integral solution of elliptic Kepler’s equation
In a recent paper, Philcox, Goodman and Slepian obtain an explicit solution of the elliptic Kepler’s equation (KE) as a quotient of two contour...
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Analytical representation of a charged black hole puncture solution
The evolution of a single uncharged black hole with the moving puncture method, considering suitable gauge conditions, leads to a time-independent...
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Extensions of a scale-separated AdS4 solution and their mass spectrum
We consider two extensions of the so-called DGKT solution, a 4d scale-separated anti-de Sitter (AdS) solution obtained as a compactification on a 6d...
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